NEW YORK -- Your average portrait photo tells you what someone looks like, right? You know it only captures a single view of them, but for now you'll buy that view as just the way things are. But what if you're presented with two shots, identical but taken a fraction of a second apart? All of a sudden there is no "way things are." The same little boy can go from looking focused and intense to looking almost tragically distracted, all because a shutter was pressed a tiny moment later. The barest lapse in time can put everything in doubt.

This is the subtle, disconcerting magic that's worked again and again in the best pieces by Roni Horn, a 54-year-old New Yorker who's a star in the art world but not much known outside it. Her 30-year retrospective at the Whitney Museum of American Art, titled "Roni Horn aka Roni Horn," ought to change that. It is one of the most fascinating shows around, if also one of the most demanding.

With Horn, it's never enough to look and move on; you have to stop and stare and contemplate. Half the pleasure in her work is how it's built to get us doing that.

Those two shots of that little boy are set among nine other pairs of images in a piece called "Becoming a Landscape." That "becoming" is the title's crucial word: The photos show how change is the one constant. The portraits -- three pairs of them -- are joined by another seven pairs of tight shots of the ground in Iceland. (Horn does a lot of her work there, maybe because the country's lively weather and geology make it one of the most changeable places on the planet.) Presented in a single image, a patch of field would just seem to be itself. Paired with a not-quite-identical twin, it stops having a clear self at all. There are now extra options: Its little pool of water can have two ripples or three; a blade of grass can be right here or just a tiny bit farther over; a fleck of sunlight can penetrate shadow or be absorbed in it. We all know the world is like this. But we're not at all used to seeing art that acknowledges this fact.

Mosaic and memory

Horn's work strikes at art's foundations. With a standard portrait or still-life or landscape, a big part of the appeal has always been the way it seems to fix a moment in the passing flux. Even abstraction can have that effect, giving a stable sense of "thusness," and so denying for a second that things might be otherwise. Horn's art insists that things are always other than they seem. That there's no fixing the flux. When she's at her best, she manages the difficult trick of using the very static mediums of photography and sculpture to deny the possibility of stasis. (There are also weak works in this show -- posh drawings and oracular text pieces -- but when has any artist got everything right?)

In a work called "This Is Me, This Is You," a grid of photos facing the elevators on the Whitney's second floor shows 48 snapshots of the artist's niece Georgia when she was about 10. Here the pictures are so different from each other they don't have the tensions of the paired photos in "Becoming." Each snapshot shows a very different aspect of the girl, from her at her most clownish, blowing bubbles with gum, to a sexy side that seems almost too old for her years. It's as though the series constructs a stable mosaic of Georgia's fixed totality, showing all the different aspects of one composite self.

Now go up to the fourth floor of the museum, where they've installed the second half of Horn's show. (Skipping the Whitney's third story was a calculated move, meant to build a sense of splitting into the structure of this survey.) In the same spot facing the elevators, you find another grid of 48 snapshots, showing the same facets of the little girl but taken with a slight time lag from the ones two floors below. The stable inventory of Georgia's girlishness is now thrown into doubt: Wasn't her face hidden by bubble gum in the last shot that you saw -- or was it? Was she really as coy as you remembered in her supermodel pose, or is that a trick of your recall? Art's supposed to help you fix the world in memory. It's not supposed to cast doubt on the whole enterprise of recollection.

Seeing is believing?

Horn's best sculptures play on similar issues. A work called "Things That Happen Again: For Two Rooms," conceived in 1986, consists of two truncated cones of solid copper, each one almost a yard long and 17 inches across at its wide end. (Picture a pair of giant megaphones.) The only difference between the two halves of the work is that one is shown in one room and the other's in the next gallery over. That simple act of separating twins breeds a constant, foiled desire to compare. Are the pieces in fact the same, or is Horn once again concealing and revealing tiny disparities? For that matter, even if the two parts have been milled as much alike as possible, do we see and feel them as different, because of the difference in setting they're seen in? Or does our mental image of the pair, as a pair, iron out any gaps in our actual perception of its two parts?

Horn doesn't even have to resort to doubling to cast doubt on stability. A work called "Asphere X" consists of a solid ball of forged stainless steel almost exactly one foot across. I say "almost," because the title tells us that the sphere is just a tiny bit off-true. Given the vagaries of light and shadow that we see it under, can we in fact perceive the flaw in this almost-spherical ovoid? Are our senses to be trusted -- ever? Or, for that matter, can we even trust an artist's pronouncements about what she's given us to see? Ought we to trust Horn's title any more than we should trust our senses? (Horn has described "Asphere" as a self-portrait, and like many of her works it can be seen as speaking to her gay identity, one that can offer a more flexible, off-kilter take on reality than a normative, straight consciousness might.)

Another sculpture, called "Pink Tons," is just a massive cube of cast pink glass, 48 inches across. This single, solid object, cast at one go, is a mess of contradictions. Its sides are rough, so frosted as to be opaque; its top is glassy-smooth and transparent. Look down into the depths of the cube and it seems both absolutely solid and entirely liquid; you can perceive fault lines between different areas inside (maybe they cooled at different speeds), but those faults have an eerie evanescence, as they get lost in a larger pool of continuous transparency. Even the shape of this object, which at first seems almost Platonic in its regularity, gets put in question: Seen from the outside it seems perfectly even and symmetrical, but peer down through the glass and the cube's bottom seems much closer than its sides.

One final piece, called "Still Water (The River Thames, for Example)," could keep you contemplating flux for hours. Fifteen photo-lithographs show different close-ups on the river in the title. That's already almost an illustration of the famous doctrine of change set forth by the Greek thinker Heraclitus: "You can never step in the same river twice." But then look closely at each print, and you realize its waters are covered with tiny numbers, and that these refer you to a crowd of footnotes printed in the bottom margin. A little "2" sends you to a note that reads, "What do you know about water? Isn't that part of what water is, that you never really know what it is?" Footnote 26 asks, "Are you following the footnotes in their proper order, or are you picking out the ones you like?" -- maybe the way you might lean over a bridge and pick a random eddy to observe, then move on to another. Footnote 27 is "(Did you notice how the numbers are floating on the paper but they're not moving?)" And 28 reads "(Did you notice how the numbers are floating in the water but they're still not moving?)"

Horn's prints perfectly capture what it is to stare at a river -- at almost any scene -- and be thoroughly absorbed in it. (In these dark prints of dark waters, suicide and death are also major themes, and feature strongly in the footnotes.) But Horn's "Still Water" also runs deep as a metaphor for our existence in the world. It lets us in on the unruly stream of consciousness that governs all our contacts with reality, but uses the rigor of footnotes to escape surrealist cliches about that stream, which can make it more absurdist than it is.

The true genius of Horn's work is that it pins down flow and change itself.

Roni Horn aka Roni Horn

runs through Jan. 24 at the Whitney Museum of American Art in New York. Call 212-570-3600 or visit http://www.whitney.org.